Using Two-Way Tables for Probability Practice Test

A random sample of 150 students recorded whether they prefer to study in the morning or evening and whether they usually study alone or in a group. Using the two-way table, what is $P(\text{Morning}\mid\text{Group})$? Give your answer as a fraction.

Two-way table (counts):

• Group & Morning: 18
• Group & Evening: 42
• Alone & Morning: 45
• Alone & Evening: 45
• Row totals: Group = 60, Alone = 90
• Column totals: Morning = 63, Evening = 87
• Grand total: 150

A random sample of 180 students was asked whether they have a part-time job (Yes/No) and whether they play a school sport (Yes/No). Using the two-way table, estimate the probability that a randomly selected student plays a school sport given that the student has a part-time job. Give your answer as a percent.

Two-way table (counts):

• Job Yes & Sport Yes: 27
• Job Yes & Sport No: 63
• Job No & Sport Yes: 54
• Job No & Sport No: 36
• Row totals: Job Yes = 90, Job No = 90
• Column totals: Sport Yes = 81, Sport No = 99
• Grand total: 180